# Properties

 Label 464968b Number of curves $2$ Conductor $464968$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("b1")

sage: E.isogeny_class()

## Elliptic curves in class 464968b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
464968.b2 464968b1 $$[0, 1, 0, -10228, -515040]$$ $$-9826000/3703$$ $$-44597989719808$$ $$$$ $$1152000$$ $$1.3289$$ $$\Gamma_0(N)$$-optimal*
464968.b1 464968b2 $$[0, 1, 0, -176288, -28545968]$$ $$12576878500/1127$$ $$54293204876288$$ $$$$ $$2304000$$ $$1.6755$$ $$\Gamma_0(N)$$-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 464968b1.

## Rank

sage: E.rank()

The elliptic curves in class 464968b have rank $$0$$.

## Complex multiplication

The elliptic curves in class 464968b do not have complex multiplication.

## Modular form 464968.2.a.b

sage: E.q_eigenform(10)

$$q - 2q^{3} - q^{7} + q^{9} + 4q^{11} - 6q^{13} + O(q^{20})$$ ## Isogeny matrix

sage: E.isogeny_class().matrix()

The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the Cremona numbering.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with Cremona labels. 